A fundamental goal in analytical chemistry is the identification and quantitative analysis of the individual components in a sample. Identification generally cannot proceed, however, until the individual components have been to some extent physically separated from one another. One of the most widely used separation techniques is chromatography. In a typical chromatographic process, a sample is passed through a tube or column containing a stationary porous medium that has a different affinity for the various components in the sample, so that the components migrate through the column at different rates. Ideally, the components become completely separated prior to emerging or eluting from the column, and can then be identified as pure chemical species by an appropriate detector positioned at the outlet. Unfortunately, complete separation or resolution of the components is the exception rather than the rule. When chromatographic resolution is very poor or nonexistent, the analyst may not even be able to know that a resolution problem exists, since two or more components will migrate at the same rate and thus be detected as if they were a single component. Even when some degree of resolution is achieved, the problem of identifying overlapped components is one that has plagued chromatography since its inception.
The process of identifying individual chemical components once they have been partially or completely separated is commonly termed detection. One common detection method for chromatography employs an optical spectrometer (e.g., ultraviolet, visible or IR) positioned at the downstream end of the chromatographic column. In a single-channel detector, the spectrometer measures the amount of radiation at a particular wavelength absorbed or emitted by the components as they elute from the column past the detector. Even when the components have been completely separated by the chromatographic column, a single-channel detector may not be capable of identifying the components, because absorption at a single wavelength is not a particularly unique identifier or signature of a chemical species. Knowledge of absorption or emission over a range of wavelengths often is a much better identifier, however, and multichannel detectors have therefore been developed that simultaneously measure the absorption or emission of eluting samples at several different wavelengths. Ideally, the components become fully separated in the chromatographic column, and each one is then uniquely identified as it passes the multichannel detector.
Another type of multichannel detector that has been widely used is the mass spectrometer. In mass spectrometry, an unknown sample is converted into an ionized gas and the ions are then separated according to their mass/charge ratios and quantified by an integral ion sensitive detector. Mass spectrometry can be used as a multichannel detection method for chromatography by periodically sampling the eluting components and analyzing the samples with a mass spectrometer to produce measurements of ion current as a function of mass/charge. Ion current and mass/charge are analogous to absorption and wavelength respectively, and mass spectometry provides comparatively unique signatures of chemical species.
While multichannel detection is an important advance, it does not directly address the problem of resolution. For example, a specific chemical component will migrate through a chromatographic column in a band of significant length. The concentration or distribution of the component within the band can be graphically represented in an idealized way by a Gaussian curve or peak, although deviations from such ideal behavior are very common. If the migration rates of two components A and B are similar, then the components may elute from the column with the trailing section of the A peak overlapping the leading section of the B peak. When these overlapped sections pass the multichannel detector, the resulting signature will be a combination of varying amounts of the pure A and B signatures, and difficult to interpret. The problem may not be serious if the overlap is slight, since there will still be times, before and after the overlapped section, when pure A and B signatures are detected. If the overlap is large, however, mathematical curve resolution may be required to resolve and identify the individual components.
One such curve resolution technique is based on principal component analysis or factor analysis. Factor analysis can be generally understood by imagining that two components have eluted from a chromatographic column at nearly the same time, and that the absorption of light by the overlapped, eluting components has been measured as a function of wavelength at 20 different time points during the interval when the components were passing a multichannel UV-VIS spectrophotometic detector. One now has, in effect, 20 sequential graphs or signatures of absorption versus wavelength. Since the measured absorption is due to two components A and B, then it should be possible to produce all 20 absorbance graphs by adding together, in varying proportions, two underlying graphs corresponding to the signatures of pure A and pure B. In many cases, methods based on factor analysis may be used to process the data represented by the 20 graphs and to find the graphs or signatures corresponding to components A and B, and thus resolving the single chromatographic peak into its separate components.
Prior techniques based on factor analysis are effective only when the components are at least partially separated by chromatography or by other separation techniques. When components elute through a chromatographic column at the same or an immeasurably different rate, however, factor analysis is unable to resolve the composite detection data into individual component signatures. It is quite common, especially in the analysis of complex mixtures, to find that many components have nearly identical migration rates, and no methods have heretofore been available for the analysis of such complex samples in an efficient manner.